The notion of ‘relation’ was defined within an MDG that has either classes or instances as nodes. Now a system will be proposed, consisting of three classifications, to provide a logical meaning to such relations: a classifi-cation of relations, a classificlassifi-cation of relation types and a classificlassifi-cation of relation type axioms. The union of the three classifications is a special type of relation ontology that will be called a Metarel ontology. It requires RDF graphs instead of MDGs for its representation. The goal of the Metarel on-tology is to formalize the logical meaning of relation types. These will be used as subjects and objects inside the Metarel ontology.
(S,P,O) Metarel: relation arc
RDF: triple
DL: assertion
P Metarel: relation type
RDF: predicate
OWL: property
DL: role
Mathematics: relation (S,O) Metarel: relation Mathematics: couple
Table 5.2: The terminology in Metarel compared with terminology in RDF, OWL, DL and Mathematics. They are compared on the basis of a generic Subject-Predicate-Object structure, as used in RDF.
5.2.1 Metarelations
Obviously certain relation types are related to each other. For example, the relation type has descendant is a supertype of the relation type has child.
The relations between relation types will be called ‘metarelations’. The creation of metarelations requires the more general RDF graph instead of an MDG.
5.2.2 Labels for relation types
Let us analyze now the following two relation arcs, or triples, represented by their labels: ‘Zeeland is part of The Netherlands’ and ‘province is part of country’. They seem to be using the same relation type is part of, but actually their relation types cannot be the same. The first ‘is part of’ must be an instance relation type, as it connects two instances, and the second
‘is part of’ must be a class relation type. Indeed we are missing some se-mantics in the sentence ‘province is part of country’. What is meant would probably be something like: ‘Every province is part of some country’.
Although both relation types may have the same label ‘is part of’, they are in fact different and they have a different identifier. It would often be hard to find human readable labels that can serve as identifiers in an RDF graph, as most quantifiers and modifiers of relations do not fit in a single triple. Sentences like ‘province all-some class relating part of country’ are
not to be preferred. For the virtues of user-friendly browsing, visualizing and text searching, it is better to hold an intuitive and consistent represen-tation with labels. A good rule for the creation of such labels is to use a verb in them, conjugated in the third person singular. Such labels may not express all the intended meaning but they lay a basis for natural language representation. The full semantics will be hidden in the identifiers of the relation types, which are formalized in the Metarel ontology. The identi-fiers can be used by visualization systems, query systems, reasoners and for Knowledge Management purposes. Natural language processing sys-tems can use the semantics of the identifiers to conjugate the verbs in the labels properly and add quantifiers like ‘every’, ‘a’, ‘some’, etc.
5.2.3 A classification of relations
As was discussed before, relation types can be ordered in a hierarchy, which has relation types as classes and relation multi-arcs (or simply relations) as instances. It corresponds to the role hierarchy in DL. This classification is important for computational reasoners, as it allows to derive supertypes from subtypes.
The assertion that a relation is an instance of a relation type, does not belong to the Metarel ontology. This is exactly what a relation arc asserts in the MDG. Only the subsumption of a relation type by another relation type needs to be asserted in the Metarel ontology.
An example is the relation between a protein type PAF1 and DNA recombination. If this relation is classified as a ‘negatively regulates’, then it is automatically also classified as a ‘regulates’.
5.2.4 A classification of relation types
The classification of relation types is a metaclassification compared to the classification of relations. An example is the classification of ‘is part of’,
‘is located in’ and ‘is preceded by’ as transitive relation types. Relation types are instances in this classification. Relation types with common se-mantic features (like reflexivity or transitivity) can be grouped in classes of relation types (like ‘reflexive relation type’ and ‘transitive relation type’).
Such classes will be called relation type classes (RTC). The whole classi-fication is shown in Figure 5.6. Multiple inheritance allows that a certain relation type instantiates several RTCs. The RTCs ‘instance relation type’,
‘class relation type’, ‘instance-class relation type’, etc. have been discussed
Relation type axiom
is a
has start
is end of
is directly preceded by
has second relation type
has first relation type
has resulting relation type
Metarel ontology
MDG ontology
is preceded by is sub
type of
breast-feeding starthas childbirth is end of pregnancy is directly preceded by
is preceded by
Figure 5.4: Two relation arcs ‘is directly preceded by’ and ‘is preceded by’
can be derived in the MDG from the classification of relations and relation type axioms in the Metarel ontology.
before. They can be classified as pairwise disjoint here.
An important subtype of relation types are those that are based on an underlying instance relation type. Such a relation type will be called an
‘instance-based relation type’. Most instance-based relation types will be instance-class relation types, class-instance relation types or class relation types, but it could also be a relation type from a more generic RTC. Metarel acknowledges that other relation types can exist between classes, instances and classes and between concepts in general. Classifying a class relation type like ‘has a longer class name than’ would not be an instance-based re-lation type. For allowing extensions ‘instance-based rere-lation type’ is added as a sibling of the other metaclasses in the hierarchy, assuming multiple in-heritance between all of them. This means that any relation type can always be classified as both an instance-based relation type and for example a class relation type.
5.2.5 A classification of relation type axioms
The semantics of a relation type is defined by relation type axioms. Some axioms apply to a single relation type (for instance ‘is part of is reflex-ive’). These axioms can be asserted by creating an appropriate RTC and classifying the relation type as one of its instances. Other axioms apply to two relation types (for instance ‘is part of is the inverse relation type of has part’). These axioms can be asserted with a metarelation between the relation types. However, there are also axioms that apply to three dif-ferent relation types, in particular for relation types that form chains. For instance the relation between two classes A and C is an is directly preceded by, whenever the relation between A and a class B is a has start and the relation between B and C is an is end of.
In a graph-based representation format, such axioms require a proper, identifiable node in the Metarel ontology, which can be connected with the relation types through metarelations. These metarelations can suffice to provide the intended meaning to the axiom (see Figure 5.4).